Apparatus-dependent contributions tog-2?

The University of Washington g-2 experiments have progressed to the marvelous precision of ${10}^{12}$ in their measurement of the magnetic moment of the electron. A further improvement of a factor of 10 should occur in the near future. Concomitant with this accuracy is the necessity of understanding small corrections. These experiments employ a Penning trap whose electrodes behave as conducting walls for a microwave cavity. We investigate the effect of this cavity on the spin and cyclotron frequencies. Previous work, employing calculations that are not gauge invariant, implies that the present level of accuracy cannot be exceeded because of cavity effects on the spin-precession frequency. In contrast to this work, we find no significant correction to the spin-precession frequency, but we do find a correction to the cyclotron frequency which may be important.